Computer generated three-dimensional models of microstructural features based on stereomicroscopy

ABSTRACT

3D information may be extracted from two 2D images by capturing a first image of a sample at a first orientation. The sample may be titled at a second or different orientation, resulting in a second image of the titled sample to be captured. Third dimension of information may be extracted from the images.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication No. 62/519,357 filed Jun. 14, 2017. The subject matter ofthis earlier filed application is hereby incorporated by reference inits entirety.

STATEMENT OF FEDERAL RIGHTS

The United States government has rights in this invention pursuant toContract No. DE-AC52-06NA25396 between the United States Department ofEnergy and Los Alamos National Security, LLC for the operation of LosAlamos National Laboratory.

FIELD

The present invention generally relates to a method for extractingthree-dimensional (3D) information from two two-dimensional (2D) images.

BACKGROUND

There are several methods to extract three-dimensional (3D) informationout of collections of two-dimensional (2D) transmission electronmicrographs. These include stereograms, weighted back projection (WBP),and simultaneous iterative reconstruction technique (SIRT) methods.There are several applications for extracting the third dimension fromtransmission electron micrographs, some of which are 3D characterizationof dislocations, second phases and irradiation defects. One of thelimitations to using weighted back projection or SIRT, is that thequality of the tomogram is related to the range of the tilt and the tiltincrement between images. Larger tilt ranges and smaller tilt incrementsproduce higher quality tomograms. Acquiring a series of images with a70° tilt range with 1° tilt increments, which is typical, limits theapplication of the technique due to the time-consuming nature.

There are methods employed to reduce the number of images required toproduce a tomogram using WBP or SIRT. For example, fiducial markers maybe placed on the image at positions of features (for example, where thedislocations end at the surfaces of the foil) which aids the alignmentof the images in the reconstruction software. By using this method,tomograms may be constructed using as few as 15 images and have enabledtomograms to be constructed at several stages during an in situstraining experiment in 304 stainless steel.

Even at 15 images, the acquisition process is time consuming. Anothersignificant drawback to conventional electron tomographic methods duringin situ straining experiments is that the image contrast should be heldconstant through the series of images acquired and deviations incontrast such as those found in images near a zone-axis in crystallinesamples should not be used. In situ strain transmission electronmicroscopy (TEM) stages almost exclusively have a single axis ofspecimen tilt with few exceptions, maintaining the same imagingconditions in crystalline samples for a necessary range of tilt is notlikely.

Stereomicroscopy for TEM gets around the necessity of acquiring tens ofimages, and instead uses 2 images. Interpretation is done by creating ananaglyph or using a stereoviewer, which still requires the two images tobe at the same diffraction conditions if the sample is crystalline.Extracting the 3D information is possible using the basis behindstereomicroscopy, the parallax, however, the process previously wastedious.

Accordingly, an improved 3D visualization software method may bebeneficial.

SUMMARY

Certain embodiments of the present invention may provide solutions tothe problems and needs in the art that have not yet been fullyidentified, appreciated, or solved by conventional fluence estimators.For example, some embodiments pertain to extracting 3D information fromtwo 2D images.

In an embodiment, a process for extracting 3D information from two 2Dimages may include capturing a first image of a sample at a firstorientation. The process also includes capturing a second image at adifferent orientation, which may be achieved by tilting the sample. Theprocess further includes extracting a third dimension of informationfrom the first and second images.

In another embodiment, a computer program for extracting 3D informationfrom two 2D images is embodied on a non-transitory medium. The computerprogram, when executed by at least one processor, is configured to causean apparatus to capture a first image of a sample at a firstorientation, and capture a second image at a different orientation,which may be achieved by tilting the sample. The computer program mayalso cause the apparatus to extract a third dimension of informationfrom the first and second image.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the advantages of certain embodiments of the inventionwill be readily understood, a more particular description of theinvention briefly described above will be rendered by reference tospecific embodiments that are illustrated in the appended drawings.While it should be understood that these drawings depict only typicalembodiments of the invention and are not therefore to be considered tobe limiting of its scope, the invention will be described and explainedwith additional specificity and detail through the use of theaccompanying drawings, in which:

FIG. 1 is a flow diagram illustrating a process for extracting 3Dinformation from a 2D image, according to an embodiment of the presentinvention.

FIG. 2A illustrates a diagram showing the principal of the parallax withrespect to embodiments of the present invention.

FIG. 2B illustrates a diagram corresponding to equations (1)-(6),according to an embodiment of the present invention.

FIG. 3 illustrates images (a)-(c), with images (a) and (b) showingBright-field TEM micrographs of dislocations observed at x-tilt valuesof 40.6° and 11.1° respectively, and image (c) showing a position of thepoints from both (a) and (b) where point P₁ is the reference point,according to an embodiment of the present invention.

FIG. 4 illustrates Bright-field TEM micrographs (images (a) and (b)) ofdislocations in two grains and a twin interface observed at x-tiltvalues of 40.6° and 11.1°, respectively, according to an embodiment ofthe present invention.

FIG. 5 illustrates select area diffraction patterns in images (a)-(d)from the grains shown in images (a)-(b) of FIG. 4, according to anembodiment of the present invention.

FIG. 6 illustrates a 3D model including crystallographic directions fromFIGS. 4 and 5, according to an embodiment of the present invention.

FIG. 7 illustrates TEM images (a)-(h) captured at a range of tilts from40.62° to −33.51°, according to an embodiment of the present invention.

FIG. 8 is a block diagram illustrating a computing system configured torun a 3D visualization software according to an embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Some embodiments generally pertain to a method and application forextracting three-dimensional (3D) data from two TEM (or othertransmission imaging techniques) images and the aid of computercalculations. This method may determine the 3D coordinates of points,such as locations along dislocations, irradiation defects, and centersof cavities, as well as locations where interfaces meet the TEM foilsurface. In certain embodiments, crystallographic information includingdislocation line directions and slip planes, interface plane normal, andthe orientation relationship between two crystals is presented. Someembodiments may also be applied to chemical maps acquired using scanningTEM with x-ray or electron energy loss spectroscopy techniques.Crystallographic information requires the additional input of twodiffraction vectors from one or two diffraction patterns for a singlecrystal beyond the two images necessary for the 3D model. By using twoimages, the acquisition times for the data set is reduced, enabling thecombination of in situ experiments such as straining or heating whileacquiring 3D information. With the assistance of a computer code, thecalculations of the 3D information can be done quickly.

Simply put, 3D information may be extracted with two 2D images capturedat different orientations. Embodiments of the present invention extractthe 3D information to create 3D representations of the 2D image. FIG. 1is a flow diagram illustrating a process 100 for extracting 3Dinformation from a 2D image, according to an embodiment of the presentinvention. In some embodiments, process 100 may begin at 105 withcapturing a first image of a sample at a first orientation. For example,by using TEM, electrons may begin on one side of the sample, go throughthe sample, and land on a detector, which is on the other side of thesample. By doing this, 2D information is received. At 110, a secondimage of the sample is captured at a second (or different) orientation.In some embodiment, the sample may be tilted with respect to theelectron beam. At 115, using the second image, a third dimension ofinformation is then extracted. For example, the third dimension ofinformation is extracted using the mathematical approach defined below.

Experimental Methods

Samples were prepared for TEM analysis by jet electropolishing. TEM maythen be performed on a FEI Tecnai T3, which operates at 300 kV.

Tomographic Method—Calculating Z

Tomograms presented and constructed of two images are based on thepremise that points in the image become closer or further away from eachother as the specimen is tilted. This effect is known as the “parallax”.When tilting in the TEM using a single axis, points in the images shiftwith respect to each other. The amount of shift is related to theposition of the point in the 3D space. A point could be where adislocation intersects either foil surface, a point along a dislocationline, the center of a precipitate or cavity, or along the line where aninterface intersects the foil surface. The third dimension of thelocation of the points is extracted by the following method.

3D position information may be extracted from the amount of tilt betweentwo micrographs and the x and y coordinates in each. First, at twovalues of tilt, the x and y coordinates of each point corresponding tofeatures in the two TEM micrographs are measured. The coordinates in thefirst and second micrographs are defined by x₁ and y₁, and x₂ and y₂,respectively. FIG. 2A illustrates the positions of two points in a TEMfoil with respect to the electron beam direction for two differentx-axis tilts of the foil. In FIG. 2A, there are two points, P₁ and P₂.From the diagram shown in FIG. 2A, it should be noted that the distancebetween P₁ and P₂ changes in the y-direction after the sample is tiltedabout the x-axis. P₁ will be referred to as the reference point and thecoordinates of P₂ will be calculated with respect to P₁ in certainembodiments. It is known from the parallax concept that Δh in FIG. 2Acan be determined by equation (1) shown below.

$\begin{matrix}{{\Delta\; h} = \frac{y_{2} - y_{1}}{2*{\sin\left( {\frac{1}{2}*\left( {\Delta\theta}_{x - {tilt}} \right)} \right)}}} & (1)\end{matrix}$

Further manipulations may permit the determination of z₁, whichcorresponds to the distance in the z direction between P₁ and P₂ at thefirst tilt frame of reference (tilt 1). The variables for the followingequations to determine the coordinates of P₂ with respect to P₁ aredefined in FIG. 2B.z ₁ =h ₀ +h ₁  (2)where

$\begin{matrix}{h_{0} = {y_{1}*{\tan\left( \frac{\Delta\;\theta_{x - {tilt}}}{2} \right)}}} & (3)\end{matrix}$and

$\begin{matrix}{h_{1} = {\frac{\Delta\; h}{\sin(\psi)} = \frac{\Delta\; h}{\sin\left( {{90{^\circ}} - \frac{\Delta\;\theta_{x - {tilt}}}{2}} \right)}}} & (4)\end{matrix}$such that

$\begin{matrix}{z_{1} = {{y_{1}*{\tan\left( \frac{{\Delta\theta}_{x - {tilt}}}{2} \right)}} + \frac{\Delta\; h}{\sin\left( {{90{^\circ}} - \frac{{\Delta\theta}_{x - {tilt}}}{2}} \right)}}} & (5)\end{matrix}$

With the measured values of x₁ and y₁ combined with the calculated z₁,the position of P₂ with respect to P₁ is provided. The reference pointP₁ has (x,y,z) position of (0,0,0). This process is used individuallyfor multiple points P₂, P₃, P₄ . . . with respect to the same referencepoint P₁ to create the tomographic model. These positions are in a frameof reference of tilt 1 shown in FIG. 2A with respect to the electronbeam.

In other embodiments, Equation (5) may be rewritten as

$\begin{matrix}{z_{1} = {\frac{y_{2}}{\sin\left( {\Delta\theta}_{x - {tilt}} \right)} - \frac{y_{1}}{\tan\left( {\Delta\theta}_{x - {tilt}} \right)}}} & (6)\end{matrix}$

FIG. 3 illustrates images (a)-(c) showing an example of what is requiredfor calculating coordinates of points along three dislocations,according to an embodiment to the present invention. The threedislocations are viewed at two x-tilts, 40.6° and 11.1°, in images (a)and (b). Image (c) shows how positions along the dislocations in image(a) shift to map onto the same position along the dislocations in image(b). Multiple positions are tracked along the dislocations with respectto the reference point P₁. Using the mathematical equations above, thecoordinates of each point with respect to P₁ may be yielded. If a largernumber of points are chosen along the dislocation line, then greaterresolution is produced in the model.

In FIG. 3(c), the shift of the points due to tilting the sample isobserved by the arrows, which are all in the same direction. Thedirection of the shift in some cases may be in both the positive andnegative direction. The direction of the shift may be determined foreach microscope and may be different for different magnificationsbecause of rotations. Finding the direction may be accomplished byoverlaying the images such that a point (reference point) is in the sameposition in the two micrographs and measuring the shift of points wheredislocations meet a surface of the foil. In some embodiments, any of thepoints may be used as a reference point. Knowing the direction of theshift is essential for calculating coordinates of positions on linessuch as positions along dislocations in the foil interior, as well aspositions along the lines of where interfaces meet a foil surface. Bymeasuring the shift and knowing the tilt, the z₁ coordinate may becalculated from equation (5) and combined with the measured x₁ and y₁coordinates.

Tomographic Method—Foil Thickness Determination

The calculated coordinates for each point may be manipulated withcoordinate transformations to determine the foil thickness. This may bedone by two rotations of the coordinates such that the z direction is inthe foil thickness direction, i.e., as if the x- and y-tilt of the foilis zero in the microscope. This may provide two advantages. First, thefoil thickness is more easily determined as the z-axis and foilthickness are in the same direction, and second, visualizing the data atspecific orientations corresponding to tilts in the microscope makeschecking the accuracy of the model easier by overlying on images notused to make the model. The two coordinate transformations, one alongthe x- and one along the y-tilt axis, according to the tilt the firstmicrograph was captured.

Tomographic Method—Reorienting Coordinates to Align with theCrystallographic Directions

Incorporating crystallographic information into the models can beachieved with diffraction spots from diffraction patterns. For example,two diffraction vectors are required and can be from different tilts ofthe specimen. The direction of each diffraction vector may be determinedby subtracting the pixel position of the transmitted beam with that ofthe diffracted beam and taking z to be zero. The direction of eachdiffraction vector is then transformed to the zero-tilt orientation suchthat the diffraction vectors directions are in the same frame ofreference as the points of the features when z is in the foil thicknessdirection. Using two additional coordinate transformations, thecoordinates of the calculated positions of features, in the zero-tiltreference frame, can then be in a reference frame such that the x, y andz coordinates of the positions are aligned with the crystallographicdirections, i.e. the x-axis is in the [100], the y-axis is in the [010],and the z-axis in the [001] crystallographic directions.

The method used for the results presented here first aligns one of thecrystallographic directions, in the zero-tilt reference frame, with acoordinate transformation such that the crystallographic direction isaligned with the x, y and z coordinates, i.e., a [111] h, k and ldiffraction vector would correspond to the vector [111] in the x, y andz coordinate system. A second crystallographic direction, in thezero-tilt reference frame, may then be transformed by the transformationrequired to align the first diffraction vector. The secondcrystallographic direction h, k and l might not match its x, y and zcoordinates. The second transformation is a rotation about the firstcrystallographic diffraction vector (after the first coordinatetransformation) at the angle required to match the second direction h, kand l to the x, y and z coordinates. Each calculated point andcrystallographic direction, in the zero-tilt frame of reference, aretransformed by the two sequential coordinate transformations resultingin the crystallographic directions aligned with the x, y and zcoordinate axis. It is crucial that the indexing of the diffractionvectors is correct.

Result—Dislocations

Dislocations and a twin boundary are shown in images (a) and (b) of FIG.4 in an Inconel 690 alloy. In FIG. 4, images (a) and (b) are 29.5° apartin tilt. It should also be noted because images (a) and (b) havedifferent diffraction contrast conditions, a model may be created withthe same or different diffraction conditions. The diffraction imagingvectors, or g-vectors, for the individual grains in both images arelabeled in FIG. 4. The points for calculating the model are along theline of the dislocations as was described above with respect to FIG. 3except that more points were used in this example. Dislocations weremodeled on both sides of the interface as well as in the interface.

Crystallographic directions were incorporated from the four diffractionpatterns, presented in images (a)-(d) of FIG. 5. The diffractionpatterns from images (a) and (b) of FIG. 5 are from the grain on theright, while images (c) and (d) of FIG. 5 are from the grain on theleft. The value of x-tilt for each diffraction pattern was captured andis also marked in FIG. 5. It should be noted that none of thediffraction information used was from a zone axis pattern, though a zoneaxis pattern would support all the diffraction information to add thecrystallographic directions. Only x-tilt was used for this experimentexhibiting the application to experiments such as in situ strainingwhere only one axis of tilt is available.

Using the incorporated crystallographic information, it was determinedthat the dislocations to the left of the twin boundary slip on the(111)_(M) plane and have line directions near [101]_(M), while those onthe right side of the interface slip on the (111)_(T) plane and haveline directions near [121]_(T). Subscripts M and T denote matrix andtwin, and were assigned to the left and right grains, respectively. Theinterface plane normal was also determined and is the (111)_(T,M) plane.

FIG. 6 illustrates a 3D model including crystallographic directions fromFIGS. 4 and 5, according to an embodiment of the present invention. InFIG. 6, dislocations, the interface and the [1,0,0], [0,1,0], and[0,0,1] crystalline directions are presented. Plotting of the calculateddata was performed using the Python Mayavi package.

Checking the accuracy of the positions may be done by overlaying themodel on images captured at various tilts. To ensure the check iscorrect, the position should undergo two coordinate transformations, onefor x-axis tilt and one for y-axis tilt, to place the z-axis in the beamdirection and the x- and y-axis such that they correspond to a foil atzero tilt. By doing this, the viewing orientation with the visualizationmethod of choice may be matched with the tilt of the various images usedfor checking. FIG. 7 illustrates images (a)-(h) captured at a range oftilts from 40.62° to −33.51°, according to an embodiment of the presentinvention. In this embodiment, images (a)-(d) are bright-fieldtransmission electron micrographs of the region of the model captured atvarious orientations (or tilts) without the 3D model overlaid. Images(e)-(h) are the images from (a)-(d) with the 3D model overlaid on theimages to show the good correlation of the model to the microstructure.

FIG. 8 is a block diagram illustrating a computing system configured torun a 3D visualization software, according to an embodiment of thepresent invention. Computing system 800 includes a bus 805 or othercommunication mechanism for communicating information, and processors810 coupled to bus 805 for processing information. Processor(s) 810include at least one CPU and at least one GPU.

Processors 810 may also have multiple processing cores, and at leastsome of the cores may be configured to perform specific functions.Multi-parallel processing may be used in some embodiments. Computingsystem 800 further includes a memory 815 for storing information andinstructions to be executed by processors 810. Memory 815 can becomprised of any combination of random access memory (RAM), read onlymemory (ROM), flash memory, cache, static storage such as a magnetic oroptical disk, or any other types of non-transitory computer-readablemedia or combinations thereof. Additionally, computing system 800includes a communication device 820, such as a transceiver and antenna,to wirelessly provide access to a communications network.

Non-transitory computer-readable media may be any available media thatcan be accessed by processors 810 and may include both volatile andnon-volatile media, removable and non-removable media, and communicationmedia. Communication media may include computer-readable instructions,data structures, program modules or other data in a modulated datasignal such as a carrier wave or other transport mechanism and includesany information delivery media.

Processors 810 are further coupled via bus 805 to a display 825, such asa Liquid Crystal Display (LCD), for displaying information to a user. Akeyboard 830 and a cursor control device 835, such as a computer mouse,are further coupled to bus 805 to enable a user to interface withcomputing system. However, in certain embodiments such as those formobile computing implementations, a physical keyboard and mouse may notbe present, and the user may interact with the device solely throughdisplay 825 and/or a touchpad (not shown). Any type and combination ofinput devices may be used as a matter of design choice.

Memory 815 stores software modules that provide functionality whenexecuted by processors 810. The modules include an operating system 840for computing system 800. The modules further include a 3D visualizationmodule 845 that is configured to perform 3D image generation byemploying any of the approaches discussed herein or derivatives thereof.Computing system 800 may include one or more additional functionalmodules 850 that include additional functionality.

One skilled in the art will appreciate that a “system” could be embodiedas an embedded computing system, a personal computer, a server, aconsole, a personal digital assistant (PDA), a cell phone, a tabletcomputing device, or any other suitable computing device, or combinationof devices. Presenting the above-described functions as being performedby a “system” is not intended to limit the scope of the presentinvention in any way but is intended to provide one example of manyembodiments of the present invention. Indeed, methods, systems andapparatuses disclosed herein may be implemented in localized anddistributed forms consistent with computing technology, including cloudcomputing systems.

It should be noted that some of the system features described in thisspecification have been presented as modules, in order to moreparticularly emphasize their implementation independence. For example, amodule may be implemented as a hardware circuit comprising custom verylarge scale integration (VLSI) circuits or gate arrays, off-the-shelfsemiconductors such as logic chips, transistors, or other discretecomponents. A module may also be implemented in programmable hardwaredevices such as field programmable gate arrays, programmable arraylogic, programmable logic devices, graphics processing units, or thelike.

A module may also be at least partially implemented in software forexecution by various types of processors. An identified unit ofexecutable code may, for instance, be comprised of one or more physicalor logical blocks of computer instructions that may, for instance, beorganized as an object, procedure, or function. Nevertheless, theexecutables of an identified module need not be physically locatedtogether but may be comprised of disparate instructions stored indifferent locations which, when joined logically together, comprise themodule and achieve the stated purpose for the module. Further, modulesmay be stored on a computer-readable medium, which may be, for instance,a hard disk drive, flash device, RAM, tape, or any other such mediumused to store data.

Indeed, a module of executable code could be a single instruction, ormany instructions, and may even be distributed over several differentcode segments, among different programs, and across several memorydevices. Similarly, operational data may be identified and illustratedherein within modules and may be embodied in any suitable form andorganized within any suitable type of data structure. The operationaldata may be collected as a single data set or may be distributed overdifferent locations including over different storage devices, and mayexist, at least partially, merely as electronic signals on a system ornetwork.

The process steps performed in FIG. 1 may be performed by a computerprogram, encoding instructions for the nonlinear adaptive processor toperform at least the process described in FIG. 1, in accordance withembodiments of the present invention. The computer program may beembodied on a non-transitory computer-readable medium. Thecomputer-readable medium may be, but is not limited to, a hard diskdrive, a flash device, a random access memory, a tape, or any other suchmedium used to store data. The computer program may include encodedinstructions for controlling the nonlinear adaptive processor toimplement the process described in FIG. 1, which may also be stored onthe computer-readable medium.

The computer program can be implemented in hardware, software, or ahybrid implementation. The computer program can be composed of modulesthat are in operative communication with one another, and which aredesigned to pass information or instructions to display. The computerprogram can be configured to operate on a general purpose computer, oran ASIC.

It will be readily understood that the components of various embodimentsof the present invention, as generally described and illustrated in thefigures herein, may be arranged and designed in a wide variety ofdifferent configurations. Thus, the detailed description of theembodiments of the present invention, as represented in the attachedfigures, is not intended to limit the scope of the invention but ismerely representative of selected embodiments of the invention.

The features, structures, or characteristics of the invention describedthroughout this specification may be combined in any suitable manner inone or more embodiments. For example, reference throughout thisspecification to “certain embodiments,” “some embodiments,” or similarlanguage means that a particular feature, structure, or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in certain embodiments,” “in some embodiment,” “in other embodiments,”or similar language throughout this specification do not necessarily allrefer to the same group of embodiments and the described features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

It should be noted that reference throughout this specification tofeatures, advantages, or similar language does not imply that all of thefeatures and advantages that may be realized with the present inventionshould be or are in any single embodiment of the invention. Rather,language referring to the features and advantages is understood to meanthat a specific feature, advantage, or characteristic described inconnection with an embodiment is included in at least one embodiment ofthe present invention. Thus, discussion of the features and advantages,and similar language, throughout this specification may, but do notnecessarily, refer to the same embodiment.

Furthermore, the described features, advantages, and characteristics ofthe invention may be combined in any suitable manner in one or moreembodiments. One skilled in the relevant art will recognize that theinvention can be practiced without one or more of the specific featuresor advantages of a particular embodiment. In other instances, additionalfeatures and advantages may be recognized in certain embodiments thatmay not be present in all embodiments of the invention.

One having ordinary skill in the art will readily understand that theinvention as discussed above may be practiced with steps in a differentorder, and/or with hardware elements in configurations which aredifferent than those which are disclosed. Therefore, although theinvention has been described based upon these preferred embodiments, itwould be apparent to those of skill in the art that certainmodifications, variations, and alternative constructions would beapparent, while remaining within the spirit and scope of the invention.In order to determine the metes and bounds of the invention, therefore,reference should be made to the appended claims.

The invention claimed is:
 1. A computer-implemented method forextracting three-dimensional (3D) data to create a 3D representationfrom two two-dimensional (2D) images, the method comprising: capturing afirst image of a sample at a first orientation; capturing a second imageat a second or different orientation from that of the first orientation;extracting 3D information using the first captured image and the secondcaptured image to create a 3D representation; incorporatingcrystallographic information into the 3D representation, wherein theincorporating of the crystallographic information comprises determininga direction of each diffraction vector by subtracting pixel position ofa transmitted beam with that of a diffracted beam and taking az-direction to be zero; transforming the direction of each diffractionvector to a zero-tilt orientation such that each diffraction vectordirection is in a same frame of reference as points of features when thez-direction is in a direction of the foil thickness; and usingcoordinate transformations to align x, y, and z coordinates of thepositions with crystallographic directions.
 2. The method of claim 1,wherein the capturing of the first image comprises using a transmissionelectron microscopy (TEM) to emit electrons from one side of the samplethrough an opposite side of the sample such that the electrons land onthe detector.
 3. The method of claim 1, wherein the capturing of thesecond image comprises tilting the sample with respect to an electronbeam emitted from a transmission electron microscopy (TEM) to capturethe second image.
 4. The method of claim 1, wherein the extracting ofthe 3D information comprises extracting 3D position information from anamount of tilt between the captured first image and the second capturedimage and x and y coordinates in each of the first image and the secondimage.
 5. The method of claim 4, wherein the extracting of the 3Dposition information comprises at two values of the tilt, measuring thex and y coordinates of each point corresponding to features in thecaptured first image and the captured second image.
 6. The method ofclaim 5, wherein the extracting of the 3D position information comprisescalculating a position of the second through last point individuallywith respect to the first point using the measured x and y coordinateswith a calculated z coordinate.
 7. The method of claim 1, furthercomprising: manipulating calculated coordinates for each point withcoordinate transformations to determine a foil thickness, wherein themanipulating comprises performing two rotations of the calculatedcoordinates, such that a z-direction is in a direction of the foilthickness and represents a zero-tilt frame of reference.
 8. Anon-transitory computer-readable medium comprising a computer programconfigured to extract 3D information from two 2D images, wherein thecomputer program, when executed by at least one processor, is configuredto capture a first image of a sample at a first orientation; capture asecond image at a second or different orientation from that of the firstorientation; extract 3D information using the first captured image andthe second captured image to create a 3D representation from the 2Dimages; index two diffraction vectors; determine a direction of eachdiffraction vector by subtracting pixel position of a transmitted beamwith that of a diffracted beam and taking a z-direction to be zero;transform the direction of each diffraction vector to a zero-tiltorientation such that each diffraction vector direction is in a sameframe of reference as points of features is the zero-tilt frame ofreference; and use coordinate transformations to align x, y, and zcoordinates of the positions with crystallographic directions.
 9. Thenon-transitory computer-readable medium of claim 8, wherein the computerprogram is further configured to use a transmission electron microscopy(TEM) to emit electrons from one side of the sample through an oppositeside of the sample such that the electrons land on the detector.
 10. Thenon-transitory computer-readable medium of claim 8, wherein the computerprogram is further configured to tilt the sample with respect to anelectron beam emitted from a transmission electron microscopy (TEM) tocapture the second image.
 11. The non-transitory computer-readablemedium of claim 8, wherein the computer program is further configured toextract 3D position information from an amount of tilt between thecaptured first image and the second captured image and x and ycoordinates in each of the first image and the second image.
 12. Thenon-transitory computer-readable medium of claim 11, wherein thecomputer program is further configured to at two values of the tilt,measure the x and y coordinates of each point corresponding to featuresin the captured first image and the captured second image.
 13. Thenon-transitory computer-readable medium of claim 12, wherein thecomputer program is further configured to calculate a position of thesecond through last point individually with respect to the first pointusing the measured x and y coordinates with a calculated z coordinate.14. The non-transitory computer-readable medium of claim 8, wherein thecomputer program is further configured to manipulate calculatedcoordinates for each point with coordinate transformations to determinea foil thickness, wherein the manipulating comprises performing tworotations of the calculated coordinates, such that a z-direction is in adirection of the foil thickness and corresponds to a zero-tilt sampleorientation in the microscope.
 15. An apparatus configured to extractthree-dimensional (3D) data to create a 3D representation from atwo-dimensional (2D) image, the method comprising: at least oneprocessor; memory comprising a set of instructions, wherein the set ofinstructions are configured to cause the processor to capture a firstimage of a sample at a first orientation; capture a second image at asecond or different orientation from that of the first orientation;extract 3D information using the first captured image and the secondcaptured image to create a 3D representation from the 2D images; indextwo diffraction vectors; determine a direction of each diffractionvector by subtracting pixel position of a transmitted beam with that ofa diffracted beam and taking a z-direction to be zero; transform thedirection of each diffraction vector to a zero-tilt orientation suchthat each diffraction vector direction is in a same frame of referenceas points of features is the zero-tilt frame of reference; and usecoordinate transformations to align x, y, and z coordinates of thepositions with crystallographic directions.
 16. The apparatus of claim15, wherein the set of instructions are further configured to cause theprocessor to use a transmission electron microscopy (TEM) to emitelectrons from one side of the sample through an opposite side of thesample such that the electrons land on the detector.
 17. The method ofclaim 15, wherein the set of instructions are further configured tocause the processor to tilt the sample with respect to an electron beamemitted from a transmission electron microscopy (TEM) to capture thesecond image.
 18. The method of claim 15, wherein the set ofinstructions are further configured to cause the processor extract 3Dposition information from an amount of tilt between the captured firstimage and the second captured image and x and y coordinates in each ofthe first image and the second image.